/*
* comp.c
*
* Functions used for compression.
*/
/*
* Copyright (C) 2012 Eric Biggers
*
* This file is part of wimlib, a library for working with WIM files.
*
* wimlib is free software; you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free
* Software Foundation; either version 3 of the License, or (at your option)
* any later version.
*
* wimlib is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License
* along with wimlib; if not, see http://www.gnu.org/licenses/.
*/
#include "comp.h"
#include
#include
static inline void flush_bits(struct output_bitstream *ostream)
{
*(u16*)ostream->bit_output = cpu_to_le16(ostream->bitbuf);
ostream->bit_output = ostream->next_bit_output;
ostream->next_bit_output = ostream->output;
ostream->output += 2;
ostream->num_bytes_remaining -= 2;
}
/* Writes @num_bits bits, given by the @num_bits least significant bits of
* @bits, to the output @ostream. */
int bitstream_put_bits(struct output_bitstream *ostream, output_bitbuf_t bits,
uint num_bits)
{
uint rem_bits;
wimlib_assert(num_bits <= 16);
if (num_bits <= ostream->free_bits) {
ostream->bitbuf = (ostream->bitbuf << num_bits) | bits;
ostream->free_bits -= num_bits;
} else {
if (ostream->num_bytes_remaining + (ostream->output -
ostream->bit_output) < 2)
return 1;
/* It is tricky to output the bits correctly. The correct way
* is to output little-endian 2-byte words, such that the bits
* in the SECOND byte logically precede those in the FIRST byte.
* While the byte order is little-endian, the bit order is
* big-endian; the first bit in a byte is the high-order one.
* Any multi-bit numbers are in bit-big-endian form, so the
* low-order bit of a multi-bit number is the LAST bit to be
* output. */
rem_bits = num_bits - ostream->free_bits;
ostream->bitbuf <<= ostream->free_bits;
ostream->bitbuf |= bits >> rem_bits;
flush_bits(ostream);
ostream->free_bits = 16 - rem_bits;
ostream->bitbuf = bits;
}
return 0;
}
/* Flushes any remaining bits in the output buffer to the output byte stream. */
int flush_output_bitstream(struct output_bitstream *ostream)
{
if (ostream->num_bytes_remaining + (ostream->output -
ostream->bit_output) < 2)
return 1;
if (ostream->free_bits != 16) {
ostream->bitbuf <<= ostream->free_bits;
flush_bits(ostream);
}
return 0;
}
/* Initializes an output bit buffer to write its output to the memory location
* pointer to by @data. */
void init_output_bitstream(struct output_bitstream *ostream, void *data,
uint num_bytes)
{
wimlib_assert(num_bytes >= 4);
ostream->bitbuf = 0;
ostream->free_bits = 16;
ostream->bit_output = (u8*)data;
ostream->next_bit_output = (u8*)data + 2;
ostream->output = (u8*)data + 4;
ostream->num_bytes_remaining = num_bytes - 4;
}
/* Intermediate (non-leaf) node in a Huffman tree. */
typedef struct HuffmanNode {
u32 freq;
u16 sym;
union {
u16 path_len;
u16 height;
};
struct HuffmanNode *left_child;
struct HuffmanNode *right_child;
} HuffmanNode;
/* Leaf node in a Huffman tree. The fields are in the same order as the
* HuffmanNode, so it can be cast to a HuffmanNode. There are no pointers to
* the children in the leaf node. */
typedef struct {
u32 freq;
u16 sym;
union {
u16 path_len;
u16 height;
};
} HuffmanLeafNode;
/* Comparator function for HuffmanLeafNodes. Sorts primarily by symbol
* frequency and secondarily by symbol value. */
static int cmp_leaves_by_freq(const void *__leaf1, const void *__leaf2)
{
const HuffmanLeafNode *leaf1 = __leaf1;
const HuffmanLeafNode *leaf2 = __leaf2;
int freq_diff = (int)leaf1->freq - (int)leaf2->freq;
if (freq_diff == 0)
return (int)leaf1->sym - (int)leaf2->sym;
else
return freq_diff;
}
/* Comparator function for HuffmanLeafNodes. Sorts primarily by code length and
* secondarily by symbol value. */
static int cmp_leaves_by_code_len(const void *__leaf1, const void *__leaf2)
{
const HuffmanLeafNode *leaf1 = __leaf1;
const HuffmanLeafNode *leaf2 = __leaf2;
int code_len_diff = (int)leaf1->path_len - (int)leaf2->path_len;
if (code_len_diff == 0)
return (int)leaf1->sym - (int)leaf2->sym;
else
return code_len_diff;
}
/* Recursive function to calculate the depth of the leaves in a Huffman tree.
* */
static void huffman_tree_compute_path_lengths(HuffmanNode *node, u16 cur_len)
{
if (node->sym == (u16)(-1)) {
/* Intermediate node. */
huffman_tree_compute_path_lengths(node->left_child, cur_len + 1);
huffman_tree_compute_path_lengths(node->right_child, cur_len + 1);
} else {
/* Leaf node. */
node->path_len = cur_len;
}
}
/* Creates a canonical Huffman code from an array of symbol frequencies.
*
* The algorithm used is similar to the well-known algorithm that builds a
* Huffman tree using a minheap. In that algorithm, the leaf nodes are
* initialized and inserted into the minheap with the frequency as the key.
* Repeatedly, the top two nodes (nodes with the lowest frequency) are taken out
* of the heap and made the children of a new node that has a frequency equal to
* the sum of the two frequencies of its children. This new node is inserted
* into the heap. When all the nodes have been removed from the heap, what
* remains is the Huffman tree. The Huffman code for a symbol is given by the
* path to it in the tree, where each left pointer is mapped to a 0 bit and each
* right pointer is mapped to a 1 bit.
*
* The algorithm used here uses an optimization that removes the need to
* actually use a heap. The leaf nodes are first sorted by frequency, as
* opposed to being made into a heap. Note that this sorting step takes O(n log
* n) time vs. O(n) time for heapifying the array, where n is the number of
* symbols. However, the heapless method is probably faster overall, due to the
* time saved later. In the heapless method, whenever an intermediate node is
* created, it is not inserted into the sorted array. Instead, the intermediate
* nodes are kept in a separate array, which is easily kept sorted because every
* time an intermediate node is initialized, it will have a frequency at least
* as high as that of the previous intermediate node that was initialized. So
* whenever we want the 2 nodes, leaf or intermediate, that have the lowest
* frequency, we check the low-frequency ends of both arrays, which is an O(1)
* operation.
*
* The function builds a canonical Huffman code, not just any Huffman code. A
* Huffman code is canonical if the codeword for each symbol numerically
* precedes the codeword for all other symbols of the same length that are
* numbered higher than the symbol, and additionally, all shorter codewords,
* 0-extended, numerically precede longer codewords. A canonical Huffman code
* is useful because it can be reconstructed by only knowing the path lengths in
* the tree. See the make_huffman_decode_table() function to see how to
* reconstruct a canonical Huffman code from only the lengths of the codes.
*
* @num_syms: The number of symbols in the alphabet.
*
* @max_codeword_len: The maximum allowed length of a codeword in the code.
* Note that if the code being created runs up against
* this restriction, the code ultimately created will be
* suboptimal, although there are some advantages for
* limiting the length of the codewords.
*
* @freq_tab: An array of length @num_syms that contains the frequencies
* of each symbol in the uncompressed data.
*
* @lens: An array of length @num_syms into which the lengths of the
* codewords for each symbol will be written.
*
* @codewords: An array of @num_syms short integers into which the
* codewords for each symbol will be written. The first
* lens[i] bits of codewords[i] will contain the codeword
* for symbol i.
*/
void make_canonical_huffman_code(uint num_syms, uint max_codeword_len,
const u32 freq_tab[], u8 lens[],
u16 codewords[])
{
/* We require at least 2 possible symbols in the alphabet to produce a
* valid Huffman decoding table. It is allowed that fewer than 2 symbols
* are actually used, though. */
wimlib_assert(num_syms >= 2);
/* Initialize the lengths and codewords to 0 */
memset(lens, 0, num_syms * sizeof(lens[0]));
memset(codewords, 0, num_syms * sizeof(codewords[0]));
/* Calculate how many symbols have non-zero frequency. These are the
* symbols that actually appeared in the input. */
uint num_used_symbols = 0;
for (uint i = 0; i < num_syms; i++)
if (freq_tab[i] != 0)
num_used_symbols++;
/* It is impossible to make a code for num_used_symbols symbols if there
* aren't enough code bits to uniquely represent all of them. */
wimlib_assert((1 << max_codeword_len) > num_used_symbols);
/* Initialize the array of leaf nodes with the symbols and their
* frequencies. */
HuffmanLeafNode leaves[num_used_symbols];
uint leaf_idx = 0;
for (uint i = 0; i < num_syms; i++) {
if (freq_tab[i] != 0) {
leaves[leaf_idx].freq = freq_tab[i];
leaves[leaf_idx].sym = i;
leaves[leaf_idx].height = 0;
leaf_idx++;
}
}
/* Deal with the special cases where num_used_symbols < 2. */
if (num_used_symbols < 2) {
if (num_used_symbols == 0) {
/* If num_used_symbols is 0, there are no symbols in the
* input, so it must be empty. This should be an error,
* but the LZX format expects this case to succeed. All
* the codeword lengths are simply marked as 0 (which
* was already done.) */
} else {
/* If only one symbol is present, the LZX format
* requires that the Huffman code include two codewords.
* One is not used. Note that this doesn't make the
* encoded data take up more room anyway, since binary
* data itself has 2 symbols. */
uint sym = leaves[0].sym;
codewords[0] = 0;
lens[0] = 1;
if (sym == 0) {
/* dummy symbol is 1, real symbol is 0 */
codewords[1] = 1;
lens[1] = 1;
} else {
/* dummy symbol is 0, real symbol is sym */
codewords[sym] = 1;
lens[sym] = 1;
}
}
return;
}
/* Otherwise, there are at least 2 symbols in the input, so we need to
* find a real Huffman code. */
/* Declare the array of intermediate nodes. An intermediate node is not
* associated with a symbol. Instead, it represents some binary code
* prefix that is shared between at least 2 codewords. There can be at
* most num_used_symbols - 1 intermediate nodes when creating a Huffman
* code. This is because if there were at least num_used_symbols nodes,
* the code would be suboptimal because there would be at least one
* unnecessary intermediate node.
*
* The worst case (greatest number of intermediate nodes) would be if
* all the intermediate nodes were chained together. This results in
* num_used_symbols - 1 intermediate nodes. If num_used_symbols is at
* least 17, this configuration would not be allowed because the LZX
* format constrains codes to 16 bits or less each. However, it is
* still possible for there to be more than 16 intermediate nodes, as
* long as no leaf has a depth of more than 16. */
HuffmanNode inodes[num_used_symbols - 1];
/* Pointer to the leaf node of lowest frequency that hasn't already been
* added as the child of some intermediate note. */
HuffmanLeafNode *cur_leaf = &leaves[0];
/* Pointer past the end of the array of leaves. */
HuffmanLeafNode *end_leaf = &leaves[num_used_symbols];
/* Pointer to the intermediate node of lowest frequency. */
HuffmanNode *cur_inode = &inodes[0];
/* Pointer to the next unallocated intermediate node. */
HuffmanNode *next_inode = &inodes[0];
/* Only jump back to here if the maximum length of the codewords allowed
* by the LZX format (16 bits) is exceeded. */
try_building_tree_again:
/* Sort the leaves from those that correspond to the least frequent
* symbol, to those that correspond to the most frequent symbol. If two
* leaves have the same frequency, they are sorted by symbol. */
qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_freq);
cur_leaf = &leaves[0];
cur_inode = &inodes[0];
next_inode = &inodes[0];
/* The following loop takes the two lowest frequency nodes of those
* remaining and makes them the children of the next available
* intermediate node. It continues until all the leaf nodes and
* intermediate nodes have been used up, or the maximum allowed length
* for the codewords is exceeded. For the latter case, we must adjust
* the frequencies to be more equal and then execute this loop again. */
while (1) {
/* Lowest frequency node. */
HuffmanNode *f1 = NULL;
/* Second lowest frequency node. */
HuffmanNode *f2 = NULL;
/* Get the lowest and second lowest frequency nodes from
* the remaining leaves or from the intermediate nodes.
* */
if (cur_leaf != end_leaf && (cur_inode == next_inode ||
cur_leaf->freq <= cur_inode->freq)) {
f1 = (HuffmanNode*)cur_leaf++;
} else if (cur_inode != next_inode) {
f1 = cur_inode++;
}
if (cur_leaf != end_leaf && (cur_inode == next_inode ||
cur_leaf->freq <= cur_inode->freq)) {
f2 = (HuffmanNode*)cur_leaf++;
} else if (cur_inode != next_inode) {
f2 = cur_inode++;
}
/* All nodes used up! */
if (f1 == NULL || f2 == NULL)
break;
/* next_inode becomes the parent of f1 and f2. */
next_inode->freq = f1->freq + f2->freq;
next_inode->sym = (u16)(-1); /* Invalid symbol. */
next_inode->left_child = f1;
next_inode->right_child = f2;
/* We need to keep track of the height so that we can detect if
* the length of a codeword has execeed max_codeword_len. The
* parent node has a height one higher than the maximum height
* of its children. */
next_inode->height = max(f1->height, f2->height) + 1;
/* Check to see if the code length of the leaf farthest away
* from next_inode has exceeded the maximum code length. */
if (next_inode->height > max_codeword_len) {
/* The code lengths can be made more uniform by making
* the frequencies more uniform. Divide all the
* frequencies by 2, leaving 1 as the minimum frequency.
* If this keeps happening, the symbol frequencies will
* approach equality, which makes their Huffman
* codewords approach the length
* log_2(num_used_symbols).
* */
for (uint i = 0; i < num_used_symbols; i++)
if (leaves[i].freq > 1)
leaves[i].freq >>= 1;
goto try_building_tree_again;
}
next_inode++;
}
/* The Huffman tree is now complete, and its height is no more than
* max_codeword_len. */
HuffmanNode *root = next_inode - 1;
wimlib_assert(root->height <= max_codeword_len);
/* Compute the path lengths for the leaf nodes. */
huffman_tree_compute_path_lengths(root, 0);
/* Sort the leaf nodes primarily by code length and secondarily by
* symbol. */
qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_code_len);
u16 cur_codeword = 0;
uint cur_codeword_len = 0;
for (uint i = 0; i < num_used_symbols; i++) {
/* Each time a codeword becomes one longer, the current codeword
* is left shifted by one place. This is part of the procedure
* for enumerating the canonical Huffman code. Additionally,
* whenever a codeword is used, 1 is added to the current
* codeword. */
uint len_diff = leaves[i].path_len - cur_codeword_len;
cur_codeword <<= len_diff;
cur_codeword_len += len_diff;
u16 sym = leaves[i].sym;
codewords[sym] = cur_codeword;
lens[sym] = cur_codeword_len;
cur_codeword++;
}
}